MM4A1: Students will explore rational functions.

MM4A1.a: Investigate and explain characteristics of rational functions, including domain, range, zeros, points of discontinuity, intervals of increase and decrease, rates of change, local and absolute extrema, symmetry, asymptotes, and end behavior.

General Form of a Rational Function
Rational Functions

MM4A1.b: Find inverses of rational functions, discussing domain and range, symmetry, and function composition.

Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Rational Functions

MM4A1.c: Solve rational equations and inequalities analytically, graphically, and by using appropriate technology.

Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

MM4A2: Students will use the circle to define the trigonometric functions.

MM4A2.a: Define and understand angles measured in degrees and radians, including but not limited to 0°, 30°, 45°, 60°, 90°, their multiples, and equivalences.

Cosine Function
Sine Function
Tangent Function

MM4A2.b: Understand and apply the six trigonometric functions as functions of general angles in standard position.

Cosine Function
Sine Function
Tangent Function

MM4A2.c: Find values of trigonometric functions using points on the terminal sides of angles in the standard position.

Cosine Function
Sine Function
Tangent Function

MM4A2.d: Understand and apply the six trigonometric functions as functions of arc length on the unit circle.

Cosine Function
Sine Function
Tangent Function
Unit Circle

MM4A2.e: Find values of trigonometric functions using the unit circle.

Cosine Function
Sine Function
Tangent Function
Unit Circle

MM4A3: Students will investigate and use the graphs of the six trigonometric functions.

MM4A3.a: Understand and apply the six basic trigonometric functions as functions of real numbers.

Cosine Function
Sine Function
Tangent Function
Unit Circle

MM4A3.b: Determine the characteristics of the graphs of the six basic trigonometric functions.

Cosine Function
Sine Function
Tangent Function
Unit Circle

MM4A3.c: Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

MM4A3.d: Apply graphs of trigonometric functions in realistic contexts involving periodic phenomena.

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions - Activity A
Unit Circle

MM4A4: Students will investigate functions.

MM4A4.a: Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise.

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratics in Factored Form
Rational Functions
Roots of a Quadratic
Sine Function
Tangent Function

MM4A4.b: Investigate transformations of functions.

Translating and Scaling Functions

MM4A4.c: Investigate characteristics of functions built through sum, difference, product, quotient, and composition.

Addition and Subtraction of Polynomials

MM4A5: Students will establish the identities below and use them to simplify trigonometric expressions and verify equivalence statements.

MM4A5.1: tan theta = sin theta/cos theta

Sine, Cosine and Tangent
Tangent Function
Tangent Ratio

MM4A5.3: sec theta = 1/cos theta

Simplifying Trigonometric Expressions

MM4A5.4: csc theta = 1/sin theta

Simplifying Trigonometric Expressions

MM4A5.5: sin² theta + cos² theta = 1

Simplifying Trigonometric Expressions

MM4A5.6: 1 + tan² theta = sec² theta

Simplifying Trigonometric Expressions

MM4A5.7: 1 + cot² theta = csc² theta

Simplifying Trigonometric Expressions

MM4A5.8: sin (alpha ± beta)= sin alpha cos beta ± cos alpha sin beta

Sum and Difference Identities for Sine and Cosine

MM4A5.9: cos (alpha ± beta) = cos alpha cos beta ± sin alpha sin beta

Sum and Difference Identities for Sine and Cosine

MM4A5.10: sin (2 theta) = 2 sin theta cos theta

Sum and Difference Identities for Sine and Cosine

MM4A5.11: cos (2 theta) = cos² theta - sin² theta

Sum and Difference Identities for Sine and Cosine

MM4A6: Students will solve trigonometric equations both graphically and algebraically.

MM4A6.b: Use the coordinates of a point on the terminal side of an angle to express x as r cos theta and y as r sin theta.

Points in Polar Coordinates

MM4A9: Students will use sequences and series

MM4A9.a: Use and find recursive and explicit formulae for the terms of sequences.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

MM4A9.b: Recognize and use simple arithmetic and geometric sequences.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

MM4A10: Students will understand and use vectors.

MM4A10.a: Represent vectors algebraically and geometrically.

Adding Vectors
Vectors

MM4A10.b: Convert between vectors expressed using rectangular coordinates and expressed using magnitude and direction.

Adding Vectors
Vectors

MM4A10.c: Add, subtract, and compute scalar multiples of vectors.

Adding Vectors
Vectors

MM4A10.d: Use vectors to solve realistic problems.

Adding Vectors
Vectors

MM4D1: Using simulation, students will develop the idea of the central limit theorem.

Probability Simulations

MM4D2: Using student-generated data from random samples of at least 30 members, students will determine the margin of error and confidence interval for a specified level of confidence.

Polling: City
Polling: Neighborhood

MM4D3: Students will use confidence intervals and margins of error to make inferences from data about a population. Technology is used to evaluate confidence intervals, but students will be aware of the ideas involved.

Polling: City